A 0.5 kg ball moving at 4 m/s collides inelastically with a 0.5 kg ball at rest. What is their combined velocity after the collision?

• A. 0 m/s
• B. 1 m/s
• C. 2 m/s
• D. 3 m/s

Answer: (C)

Momentum conservation is key here: with no external forces, the total momentum before a collision equals the total momentum after.

The moving ball has momentum (0.5 kg)(4 m/s) = 2 kg·m/s, and the resting ball has none. So the initial total momentum is 2 kg·m/s. After they collide and stick together, their combined mass is 1.0 kg, moving at velocity v. The final momentum is (1.0 kg)·v, which must equal the initial 2 kg·m/s. So v = 2 m/s.

Thus the two balls move together at 2 m/s. Inelastic collisions conserve momentum but not kinetic energy, which is why energy decreases even though the momentum stays the same.